Theorem REF (i) and (ii) indicate that the larger the batch size \(b\)  is, the smaller the upper bounds of the performance measures become. From (i), it would be desirable to use small learning rates \(\alpha ^G\)  and \(\alpha ^D\) . Meanwhile, (ii) indicates that there is no evidence that using sufficiently small \(\alpha ^G\)  and \(\alpha ^D\)  is good for training GANs since the upper bounds in Theorem REF  depend on \(\alpha ^G\) , \(\alpha ^D\) , \(1/\alpha ^G\) , and \(1/\alpha ^D\) . Indeed, the results reported in [1]} used small \(\alpha ^G, \alpha ^D = 10^{-4}, 10^{-5}\) .
